Dissipation-Shaped Quantum Geometry in Nonlinear Transport

Area of Science:

• Condensed matter physics
• Quantum geometry
• Quantum transport

Background:

• The intrinsic nonlinear Hall effect is crucial for understanding quantum geometry.
• Existing theories present conflicting expressions for dissipation-independent conductivity.
• This ambiguity hinders a universal understanding of the phenomenon.

Purpose of the Study:

• To resolve ambiguities in the theory of the intrinsic nonlinear Hall effect.
• To clarify the dependence of the nonlinear Hall conductivity on dissipation mechanisms.
• To establish a benchmark for the exact calculation of this conductivity.

Main Methods:

• Solving the exact nonequilibrium steady state (NESS) density matrix for a generic Bloch system.
• Coupling the system to a featureless fermionic bath.
• Analyzing the decomposition of the conductivity into geometric and kinetic parts.

Main Results:

• The intrinsic nonlinear Hall conductivity is not universal and depends on the dissipation mechanism.
• The exact conductivity decomposes into a geometric part (σgeo) and a novel kinetic part (σkin).
• The geometric part clarifies inconsistencies related to the quantum metric, while the kinetic part arises from modified occupation functions.

Conclusions:

• The nonlinear Hall conductivity is contingent on the physical system-bath coupling, not solely the Bloch Hamiltonian.
• Dissipation mechanisms uniquely shape the NESS density matrix, influencing the conductivity.
• This work provides a definitive framework for understanding intrinsic nonlinear Hall conductivity.